Ivan Andrus (CEU): Some dualities between conjugacy classes and
Robinson has shown that the character degrees are determined by
knowing, for all n, the number of ways that the identity can be
expressed as a product of n commutators. Earlier, Strunkov showed that
the existence of characters of p-defect 0 can be determined by counting
solutions to certain equations involving commutators and conjugates.
In this paper, we prove analogs to Robinson's and Strunkov's theorems
by switching conjugacy classes and characters. We show that counting
the multiplicity of the trivial character in certain products of
characters determines the conjugacy class sizes and existence of
conjugacy classes with p-defect 0.